Recent theoretical literature studies how labor market reforms in one country can affect labor market outcomes in other countries, thereby rationalizing widely-held policy beliefs and empirical evidence. But what is the quantitative relevance of such spillover effects? This paper combines two recent workhorse models: the canonical search-and-matching framework and the heterogeneous firms international trade model. Qualitatively, the framework confirms that labor market reforms in one country benefit its trading partners, replicating the stylized facts. However, when wages are bargained flexibly, the model quantitatively underestimates the correlation of structural unemployment rates across countries. This mirrors the well-known finding by Shimer (2005) by which the standard search-and-matching model predicts too small fluctuations of unemployment rates over time. Introducing real wage rigidity remedies this problem.